CN110927659B - Method and system for estimating arbitrary array manifold DOA (direction of arrival) under cross-coupling condition and cross-coupling calibration - Google Patents

Method and system for estimating arbitrary array manifold DOA (direction of arrival) under cross-coupling condition and cross-coupling calibration Download PDF

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CN110927659B
CN110927659B CN201911165917.6A CN201911165917A CN110927659B CN 110927659 B CN110927659 B CN 110927659B CN 201911165917 A CN201911165917 A CN 201911165917A CN 110927659 B CN110927659 B CN 110927659B
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向全伟
文方青
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Yangtze University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/08—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station
    • H04B7/0837—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas at the receiving station using pre-detection combining
    • H04B7/0842—Weighted combining
    • H04B7/086—Weighted combining using weights depending on external parameters, e.g. direction of arrival [DOA], predetermined weights or beamforming
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
    • G01S3/023—Monitoring or calibrating
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/10—Monitoring; Testing of transmitters
    • H04B17/11—Monitoring; Testing of transmitters for calibration
    • H04B17/12—Monitoring; Testing of transmitters for calibration of transmit antennas, e.g. of the amplitude or phase
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/78—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using electromagnetic waves other than radio waves
    • G01S3/7803—Means for monitoring or calibrating
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
    • G01S3/80—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using ultrasonic, sonic or infrasonic waves
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/20—Monitoring; Testing of receivers
    • H04B17/21—Monitoring; Testing of receivers for calibration; for correcting measurements
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B17/00—Monitoring; Testing
    • H04B17/30—Monitoring; Testing of propagation channels
    • H04B17/309—Measuring or estimating channel quality parameters
    • H04B17/336—Signal-to-interference ratio [SIR] or carrier-to-interference ratio [CIR]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04B—TRANSMISSION
    • H04B7/00—Radio transmission systems, i.e. using radiation field
    • H04B7/02—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas
    • H04B7/04—Diversity systems; Multi-antenna system, i.e. transmission or reception using multiple antennas using two or more spaced independent antennas
    • H04B7/0413—MIMO systems
    • H04B7/0426—Power distribution
    • H04B7/043—Power distribution using best eigenmode, e.g. beam forming or beam steering

Abstract

The invention discloses a method and a system for estimating and calibrating free array manifold DOA under a mutual coupling condition, belongs to the technical field of array sensor direction finding, and solves the problem that the complexity of calculation of the free array manifold DOA estimation and the mutual coupling calibration under the mutual coupling condition is too large in the prior art. A method for estimating and calibrating manifold DOA of any array under a mutual coupling condition comprises the following steps: acquiring an array signal, estimating according to the array signal to obtain a covariance matrix corresponding to the array signal, and performing characteristic decomposition on the covariance matrix to obtain a noise subspace; determining the angle search range of the DOA, generating a group of grids according to the angle search range of the DOA, and acquiring a spectrum function corresponding to each grid according to a noise subspace and a cross coupling matrix between array elements; and estimating to obtain DOA according to the peak value of the spectrum function corresponding to each grid, and acquiring the mutual coupling coefficient between the array elements by the DOA obtained by estimation. The method has the advantage that the estimation and mutual coupling calibration of the manifold DOA of any array under the mutual coupling condition are realized more simply.

Description

Method and system for estimating arbitrary array manifold DOA (direction of arrival) under cross-coupling condition and cross-coupling calibration
Technical Field
The invention relates to the technical field of array sensor direction finding, in particular to a method and a system for estimating and calibrating arbitrary array manifold DOA under a mutual coupling condition.
Background
Signal angle of arrival (DOA) estimation has a long history of over 60 years, and a number of excellent angle estimation methods, such as multiple signal classification (MUSIC) algorithm and a method of estimating signal parameters by rotation invariant feature (ESPRIT), have emerged. However, the excellent performance of the existing methods is obtained under ideal array conditions. In practice, sensor errors are always present. Typical sensor errors include gain phase error, position error, and mutual coupling effects. Mutual coupling effects are a common type of array error, among others. Mutual coupling effects between sensors are caused by coupling effects of array antenna elements, which can cause model mismatch in DOA estimation and may cause severe degradation of estimation performance. In order to obtain the best DOA estimation, a self-calibration function needs to be established in the sensor array, and the sensor error is calibrated while the signals are acquired by the sensor array. The joint DOA estimation and mutual coupling error calibration problem has attracted a wide range of attention.
In the prior art, an active calibration method is adopted, but an additional auxiliary array element is required, an iterative algorithm of joint estimation of DOA and mutual coupling coefficient without an auxiliary source or an auxiliary array element is also adopted, but the iterative process is low in calculation efficiency, in order to effectively reduce the calculation amount, a recursive rank reduction method is deduced, in addition, researchers research DOA estimation and mutual coupling calibration problems from the perspective of bayesian learning, and an improved bayesian learning algorithm is also adopted, so that the problem of net separation can be solved, but the solution is suitable for special array manifolds, such as Uniform Linear Arrays (ULA), Uniform rectangular arrays, Uniform circular arrays and the like, in the case that array mutual coupling is modeled as a matrix with a special structure, such as a symmetric Toeplitz matrix, a symmetric cycle matrix or a symmetric block toetz matrix,
in practical engineering, due to space constraints, the sensor array may be distributed in an irregular array manifold. At the moment, the mutual coupling matrix has almost no other special structures except symmetry, and the conventional method can realize the purposes of DOA estimation and mutual coupling error calibration; in order to reduce the mutual coupling effect in the DOA estimation, a two-step iteration method is proposed, which is suitable for array manifold with arbitrary geometry, but the iterative computation complexity in the method is too large to be used in a real-time system.
Disclosure of Invention
The present invention is directed to overcome at least one of the above technical deficiencies, and to provide a method and a system for estimating and calibrating DOA of arbitrary array manifold under cross-coupling condition.
In one aspect, the invention provides a method for estimating and calibrating free array manifold DOA under a mutual coupling condition, which comprises the following steps:
obtaining an array signal, estimating according to the array signal to obtain a covariance matrix corresponding to the array signal, and performing characteristic decomposition on the covariance matrix to obtain a noise subspace;
determining the angle search range of the DOA, generating a group of grids according to the angle search range of the DOA, and acquiring a spectrum function corresponding to each grid according to the noise subspace and a mutual coupling matrix between array elements;
and estimating to obtain DOA according to the peak value of the spectrum function corresponding to each grid, and acquiring the mutual coupling coefficient between the array elements by the DOA obtained by estimation.
Further, performing feature decomposition on the covariance matrix to obtain a noise subspace, specifically including,
Figure GDA0003388351630000021
wherein the content of the first and second substances,
Figure GDA0003388351630000022
is a covariance matrix alpha1≥α2≥...≥αK≥αK+1≥...≥αMIs an eigenvalue, u, of a covariance matrixm∈￡M×1For eigenvectors corresponding to eigenvalues of the covariance matrix, Us＝[u1,u2,...,uK]，Σs＝diag{α1,α2,...,αK}，Un＝[uK+1,uK+2,...,uM]，Σn＝diag{αK+1,αK+2,...,αM}，UsAnd UnRespectively a signal subspace and a noise subspace.
Further, obtaining a spectrum function corresponding to each grid according to the noise subspace and the mutual coupling matrix among the array elements, specifically comprising,
using max dHQ-1(Θ) d obtaining a spectral function corresponding to each grid, wherein,
Figure GDA0003388351630000023
T(:,q)＝Jqa，a∈￡M×M，
Figure GDA0003388351630000024
d＝[1,0,...,0]T，q＝1,2,3...,Q， Q<m, C are cross-coupling matrices between array elements, UnIs a noise subspace, T ∈ CM×Q，c＝[c1,c2,..,cQ]TT (: q) is the q-th row of T, n is more than or equal to 1, and M is more than or equal to M.
Further, the mutual coupling coefficient between array elements is obtained by the estimated DOA, specifically including,
using formulas
Figure GDA0003388351630000031
And obtaining the mutual coupling coefficient between array elements, wherein,
Figure GDA0003388351630000032
for the mutual coupling coefficient, p is a constant,
Figure GDA0003388351630000033
is the estimated DOA.
On the other hand, the invention also provides a system for estimating and calibrating the DOA of any array manifold under the mutual coupling condition, which comprises a noise subspace acquisition module, a spectrum function acquisition module, a DOA and mutual coupling coefficient acquisition module,
the noise subspace acquisition module is used for acquiring an array signal, obtaining a covariance matrix corresponding to the array signal according to the array signal estimation, and performing feature decomposition on the covariance matrix to obtain a noise subspace;
the spectrum function acquisition module is used for determining the angle search range of the DOA, generating a group of grids according to the angle search range of the DOA, and acquiring a spectrum function corresponding to each grid according to the noise subspace and the cross coupling matrix among the array elements;
and the DOA and mutual coupling coefficient acquisition module is used for estimating and obtaining the DOA according to the peak value of the spectrum function corresponding to each grid and acquiring the mutual coupling coefficient between the array elements according to the estimated DOA.
Further, the noise subspace obtaining module performs feature decomposition on the covariance matrix to obtain a noise subspace, specifically including,
Figure GDA0003388351630000034
wherein the content of the first and second substances,
Figure GDA0003388351630000035
is a covariance matrix alpha1≥α2≥...≥αK≥αK+1≥...≥αMIs an eigenvalue, u, of a covariance matrixm∈￡M×1For eigenvectors corresponding to eigenvalues of the covariance matrix, Us＝[u1,u2,...,uK]，Σs＝diag{α1,α2,...,αK}，Un＝[uK+1,uK+2,...,uM]，Σn＝diag{αK+1,αK+2,...,αM}，UsAnd UnRespectively a signal subspace and a noise subspace.
Further, the spectrum function obtaining module obtains the spectrum function corresponding to each grid according to the noise subspace and the cross-coupling matrix among the array elements, specifically including,
using max dHQ-1(Θ) d obtaining a spectral function corresponding to each grid, wherein,
Figure GDA0003388351630000036
T(:,q)＝Jqa，a∈￡M×M，
Figure GDA0003388351630000037
d＝[1,0,...,0]T，q＝1,2,3...,Q， Q<m, C are cross-coupling matrices between array elements, UnIs a noise subspace, T ∈ CM×Q，c＝[c1,c2,...,cQ]TT (: q) is the q-th row of T, n is more than or equal to 1, and M is more than or equal to M.
Further, the module for obtaining DOA and mutual coupling coefficient obtains mutual coupling coefficient between array elements according to DOA obtained by estimation, specifically including using formula
Figure GDA0003388351630000041
And obtaining the mutual coupling coefficient between array elements, wherein,
Figure GDA0003388351630000042
for the mutual coupling coefficient, p is a constant,
Figure GDA0003388351630000043
for estimating the resulting DOA
Compared with the prior art, the invention has the beneficial effects that: obtaining an array signal, estimating according to the array signal to obtain a covariance matrix corresponding to the array signal, and performing characteristic decomposition on the covariance matrix to obtain a noise subspace; determining the angle search range of the DOA, generating a group of grids according to the angle search range of the DOA, and acquiring a spectrum function corresponding to each grid according to the noise subspace and a mutual coupling matrix between array elements; and estimating to obtain DOA according to the peak value of the spectrum function corresponding to each grid, and acquiring the mutual coupling coefficient between array elements by the DOA obtained by estimation, thereby simply realizing the DOA estimation and the mutual coupling calibration of any array manifold under the mutual coupling condition.
Drawings
FIG. 1 is a flow chart of a method for estimating and calibrating free-form array manifold DOA under mutual coupling conditions according to embodiment 1 of the present invention;
FIG. 2 is a schematic illustration of a ULA as described in example 1 of the present invention;
FIG. 3 is a schematic illustration of a 3D-ULA as described in example 1 of the present invention;
FIG. 4 is a comparison graph of spatial spectra in the case of scenario 1 according to the embodiment of the present invention;
FIG. 5 is a spatial spectrum diagram in a second scenario described in embodiment 1 of the present invention;
FIG. 6 is a graph of RMSE versus SNR for DOA estimation under scenario 1 of the present invention;
FIG. 7 is a graph of RMSE versus SNR for mutual coupling estimation under a scenario 1 in accordance with an embodiment of the present invention;
FIG. 8 is a diagram of RMSE versus SNR for DOA estimation in case of scenario two as described in embodiment 1 of the present invention;
FIG. 9 is a graph of the RMSE versus SNR for the mutual coupling estimation in the second scenario of embodiment 1 of the present invention;
FIG. 10 is a diagram of RMSE versus M for DOA estimation under scenario 1 of the present invention;
FIG. 11 is a graph of RMSE versus M for mutual coupling coefficient estimation under a scenario described in embodiment 1 of the present invention;
FIG. 12 is a graph of average runtime versus M for the scenario described in embodiment 1 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Example 1
The embodiment of the invention provides a method for estimating and calibrating free array manifold DOA under a mutual coupling condition, which comprises the following steps:
obtaining an array signal, estimating according to the array signal to obtain a covariance matrix corresponding to the array signal, and performing characteristic decomposition on the covariance matrix to obtain a noise subspace;
determining the angle search range of the DOA, generating a group of grids according to the angle search range of the DOA, and acquiring a spectrum function corresponding to each grid according to the noise subspace and a mutual coupling matrix between array elements;
and estimating to obtain DOA according to the peak value of the spectrum function corresponding to each grid, and acquiring the mutual coupling coefficient between the array elements by the DOA obtained by estimation.
In specific implementation, K uncorrelated sources are incident on a far field of a certain array in space, the array antenna is composed of M array elements, ideally, the array elements are distributed in a 3D space, and the coordinate of the M (M is 1,2m＝[xm,ym,zm]TUsing thetak＝[θk,φk]TTo denote the DOA pair (or DOA), θ, of the K (K ═ 1,2, …, K) th signal sourcekAnd phikRespectively representing a Kth pitch angle and a Kth azimuth angle; the acquired array signal can be expressed as
Figure GDA0003388351630000051
Wherein, a (theta)k)＝[exp{-j2πτ1,k/λ},exp{-j2πτ2,k/λ},...,exp{-j2πτM,k/λ}]T∈￡M×1Is the response vector of the Kth uncorrelated source, λ is the carrier wavelength, sk(t) is the Kth baseband signal, n (t) is array noise £ £M×1A complex matrix of mx 1;
Α＝[a(Θ1),a(Θ2),...,a(ΘK)]∈￡M×Kis a direction matrix, s (t) ═ s1(t),s2(t),..,sK(t)]TIs a signal source matrix;
τm,khas the following form
Figure GDA0003388351630000052
Wherein r isk@[cos(φk)sin(θk),cos(φk)sin(θk),cos(θk)]TWhen the mutual coupling effect exists between array elements, the signal expression (1) is invalid; introducing Mm × Mm cross coupling matrix C to describe cross coupling effect between Mm array elements
Figure GDA0003388351630000061
Wherein C at (p, q) in CmIs the mutual coupling coefficient between the p array element and the q array element; under ideal conditions, cmIs inversely proportional to the distance between array elements; in practical cases, if the distance is greater than a given threshold, the mutual coupling coefficient is approximately 0; from expression (3), C is a symmetric matrix and is for an arbitrary m>1 all have | cm|<c 11 is ═ 1; obviously, at most only C
Figure GDA0003388351630000062
A plurality of different entities; due to the recognition capability, C is assumed to have at most Q ═ M-K different elements; at this time, the array signal in expression (1) can be rewritten as
x(t)＝CAs(t)+n(t) (4)
If n (t) is white Gaussian noise and is uncorrelated with s (t) signal source, the covariance matrix of x (t) can be expressed as
R＝CARsAHCH+σ2IM (5)
In the formula, Rs＝diag{δ1,δ2,...,δKIs the covariance matrix of the signal source s (t), δKIs the power of the Kth signal source, and sigma is the noise variance; when the fast beat number L is given, let t be 1,2, …, L, the covariance matrix R can be estimated by the following equation
Figure GDA0003388351630000063
Preferably, the feature decomposition is performed on the covariance matrix to obtain a noise subspace, specifically including,
Figure GDA0003388351630000064
wherein the content of the first and second substances,
Figure GDA0003388351630000065
is a covariance matrix alpha1≥α2≥...≥αK≥αK+1≥...≥αMIs an eigenvalue, u, of a covariance matrixm∈￡M×1For eigenvectors corresponding to eigenvalues of the covariance matrix, Us＝[u1,u2,...,uK]，Σs＝diag{α1,α2,...,αK}，Un＝[uK+1,uK+2,...,uM]，Σn＝diag{αK+1,αK+2,...,αM}，UsAnd UnRespectively a signal subspace and a noise subspace.
Specific embodiment, UsAnd UnAre orthogonal to each other, UsOpens the same space as the matrix CA, so
Figure GDA0003388351630000071
If the signal DOA is estimated using the MUSIC method, the group needs to calculate the ordinary function as follows
Figure GDA0003388351630000072
In general, all grids possibly consisting of DOA are set, and by finding the spectral peak of expression (9), the DOA signal can be estimated; however, since the cross-coupling matrix C is unknown, the conventional MUSIC method cannot be used;
preferably, the obtaining of the spectrum function corresponding to each grid according to the noise subspace and the mutual coupling matrix between the array elements specifically includes,
using max dHQ-1(Θ) d, a spectral function corresponding to each grid, wherein,
Figure GDA0003388351630000073
T(:,q)＝Jqa，a∈￡M×M，
Figure GDA0003388351630000074
d＝[1,0,...,0]T，q＝1,2,3...,Q，Q<m, C are cross-coupling matrices between array elements, UnIs a noise subspace, T ∈ CM×Q，c＝[c1,c2,...,cQ]TT (: q) is the q-th row of T, n is more than or equal to 1, and M is more than or equal to M.
In specific implementation, for the mutual coupling matrix C epsilon £ £M×MAnd vector a ∈ £M×MIf only Q (Q) is present in C<M) different elements c ═ c1,c2,...,cQ]TThen there is the following transformation
Ca＝Tc (10)
Wherein T is epsilonM×QColumn Q (Q is 1,2, …, Q) is given by
T(:,q)＝Jqa (11)
JqIs defined as
Figure GDA0003388351630000075
And is also provided with
Ca(Θ)＝T(Θ)c (13)
In the formula, T (theta) belongs to E £M×QAnd c ∈ £ cQ×1(ii) a Thus, expression (9) may be modified to
Figure GDA0003388351630000076
Can order
Figure GDA0003388351630000081
It is clear that expression (14) is a quadratic optimization problem, and that constraint conditions may be enforced in order to avoid having no solution when c is 0
dHc＝ρ (15)
Where ρ is a constant and d is [1,0, … 0 ]]TSo expression (15) can be converted into
min cHQ(Θ)c s.t.,dHc/ρ＝1 (16)
It should be noted that s.t. is an expression symbol of a constraint condition, the above problem can be solved by a lagrangian multiplier method, and a lagrangian function is constructed
Figure GDA0003388351630000087
Where τ is the Lagrangian multiplier, then let
Figure GDA0003388351630000082
Namely, it is
Figure GDA0003388351630000083
Thereby can obtain
c＝ξQ-1(Θ)d/ρ (19)
Where xi is a constant, expression (19) in combination with expression (15) having
Figure GDA0003388351630000084
Substituting expression (20) into expression (19) can obtain
Figure GDA0003388351630000085
Finally, we can rewrite expression (16) to
Figure GDA0003388351630000086
Since ρ is constant, the expression (22) is again equal to
max dHQ-1(Θ)d (23)
Preferably, the mutual coupling coefficient between the array elements obtained by the estimated DOA specifically includes,
using formulas
Figure GDA0003388351630000091
And obtaining the mutual coupling coefficient between array elements, wherein,
Figure GDA0003388351630000095
for the mutual coupling coefficient, p is a constant,
Figure GDA0003388351630000092
is the estimated DOA. It should be noted that the DOA pair (or DOA) can be estimated by K spectral peaks of expression (23), if c1Then the scaling effect in expression (24) can be removed by a normalization operation.
In the absence of noise, the noise can be reduced
cHQ(Θ)c＝0 (25)
When c ≠ 0, the essential condition for expression (25) is that Q (Θ) has rank deficiency, i.e.
det{Q(Θ)}＝0 (26)
The method of DOA estimation may be replaced with one according to expression (27)
Figure GDA0003388351630000093
In order to illustrate the performance of the arbitrary array manifold DOA estimation and cross-coupling calibration method under the cross-coupling condition according to the embodiment of the present invention, the arbitrary array manifold DOA estimation and cross-coupling calibration method under the cross-coupling condition (hereinafter, all referred to as the method of the present invention) is compared with the conventional MUSIC method (labeled as MUSIC), the iterative method (labeled as the iterative method), and the cramer-circle boundary (labeled as CRB).
In one implementation, there are M array elements and K far field sources; the source signal meets normal distribution, and the data of taking a snapshot for 200 times is collected; the signal-to-noise ratio (SNR) in the simulation was defined as
Figure GDA0003388351630000094
All simulations were run on an HP Z840 system (containing two Intel (R) Xeon (R) E5-2650 v42.20GHz processors, 128GB DDR4 RAM) and MATLAB R2016 a; the cross-coupling simulation scenarios of the embodiment of the present invention are two, respectively,
scenario one, in ULA, the distance between array elements is λ/2, and the schematic diagram of ULA is shown in fig. 2, where Q is 3 and c is [1,0.8+0.5j,0.2+0.1j in simulation]TIn this case, DOA estimation can be performed only by estimating the azimuth angle θ;
scene two, in the 3D-ULA, the distance between the array elements is λ/2, and there are M ═ 12 array elements, a schematic diagram of the 3D-ULA, as shown in fig. 3; c is assumed as the mutual coupling coefficient between two adjacent array elements20.8+0.5j, the mutual coupling coefficient between two array elements at a distance λ is c30.017+0.035j, and the mutual coupling coefficient between two array elements which are 'cross-adjacent' is c40.2+0.1 j; thus, Q ═ 4 and c ═ 1,0.8+0.5j,0.017+0.035j,0.2+0.1j]T(ii) a Further, it is assumed that K — 2 signal sources are located at Θ ═ 40 °, 25 °, and Θ ═ 60 °, 105 °, respectively.
In the first embodiment, in the case of scene one, the spatial spectrums of the method, the MUSIC method and the iterative method of the present invention are compared; more precisely, the real values of DOA are 20 °, 25 °, 40 ° when M is 12, SNR is 20dB and K is 3, respectively; the angle search range for all methods is [0 °, 90 ° ], with a grid spacing of 0.1 °. And 5 independent tests were performed for each method; a spatial spectrum comparison diagram under the condition of a scene one is obtained, as shown in fig. 4, it can be found from fig. 4 that the conventional MUSIC method cannot normally operate; however, the method and iterative method of the present invention both provide good performance because they are powerful enough to resist the mutual coupling effect.
In a second specific example, the performance of the method of the present invention in the case of scenario two was tested, wherein the SNR was considered to be 10dB, the search range of θ was [0 °, 90 ° ], the grid spacing was 0.5 °, the search range of Φ was [0 °, 180 ° ], the grid spacing was 1 °, and a spatial spectrogram in the case of scenario two was obtained, as shown in fig. 5; it is clear that the method of the present invention is capable of correctly detecting and pairing two-dimensional (2D) DOAs.
In a third specific example, in a case of a test scenario, Root Mean Square Error (RMSE) performance is measured for three methods, where DOA estimates are 20 ° and 30 ° respectively when M is 12 and K is 2, and the angle search ranges of the three methods are [0 °, 90 ° ], and the interval is 0.1 °; the relationship between the RMSE curves of the DOA estimation and the mutual coupling coefficient estimation and the SNR is calculated by using 500 independent experiments, and the relationship between the RMSE and the SNR of the DOA estimation in the case of the scene one and the relationship between the RMSE and the SNR of the mutual coupling estimation in the case of the scene one are respectively shown in fig. 6 and fig. 7; (the performance of the MUSIC approach is not given in fig. 7, since conventional MUSIC does not provide a mutual coupling estimate); the results show that the traditional MUSIC method cannot work under such conditions; compared with an iteration method, when the SNR is less than 1dB, the method of the invention provides better DOA estimation performance, and when the SNR is more than 5dB, the method of the invention provides slightly better RMSE performance; however, for the estimation of the mutual coupling coefficient, the advantages of the method of the present invention are not obvious, because the absolute value of the mutual coupling coefficient is usually less than 1, and therefore the absolute error is relatively small, as shown in fig. 7.
In a fourth embodiment, the above simulation is repeated using scenario two, where θ is searched for in a range of [20 °, 80 ° ], with an interval of 0.2 °, and Φ is searched for in a range of [0 °, 130 ° ], with an interval of 0.5 °, to obtain an RMSE curve for DOA estimation, and in scenario two, the RMSE versus SNR plot for DOA estimation is shown in fig. 8, from which it can be clearly seen that the conventional MUSIC method does not operate normally, and furthermore, the iterative method provides slightly better DOA estimation performance than the method of the present invention, but both can obtain CRB; the RMSE versus SNR for the mutual coupling estimation for scenario two, as shown in fig. 9; the RMSE of the method is slightly better than that of an iterative algorithm, and the method has performance difference with CRB.
In the fifth embodiment, under the condition of the first scenario, the relationship between the performance of different methods and the array element number M is tested, wherein, assuming that the SNR is 10dB, other conditions are the same as those in the third embodiment, the relationship diagram between the RMSE and M for DOA estimation under the first scenario and the relationship diagram between the RMSE and M for mutual coupling coefficient estimation under the first scenario are shown in fig. 10 and 11, respectively; FIGS. 10 and 11 show the RMSE for DOA estimation and the RMSE for mutual coupling estimation, respectively; it was found in the simulation that as M increases, the RMSE of the DOA estimate gradually decreases, while the RMSE of the cross-coupling estimate hardly changes with M, so the method of the present invention performs better than the iterative method, comparing the mean run time of the method of the present invention and the iterative method yields a plot of mean run time versus M for the case of scenario, as shown in fig. 12, from which it can be seen that the method of the present invention is computationally more efficient than the iterative method.
Example 2
The embodiment of the invention provides a DOA estimation and cross coupling calibration system for arbitrary array manifold under the cross coupling condition, which comprises a noise subspace acquisition module, a spectrum function acquisition module, a DOA and cross coupling coefficient acquisition module,
the noise subspace acquisition module is used for acquiring an array signal, obtaining a covariance matrix corresponding to the array signal according to the array signal estimation, and performing feature decomposition on the covariance matrix to obtain a noise subspace;
the spectrum function acquisition module is used for determining the angle search range of the DOA, generating a group of grids according to the angle search range of the DOA, and acquiring a spectrum function corresponding to each grid according to the noise subspace and the cross coupling matrix among the array elements;
and the DOA and mutual coupling coefficient acquisition module is used for estimating and obtaining the DOA according to the peak value of the spectrum function corresponding to each grid, and acquiring the mutual coupling coefficient between the array elements according to the estimated DOA.
Preferably, the noise subspace obtaining module performs characteristic decomposition on the covariance matrix to obtain a noise subspace, specifically including,
Figure GDA0003388351630000111
wherein the content of the first and second substances,
Figure GDA0003388351630000121
is a covariance matrix alpha1≥α2≥...≥αK≥αK+1≥...≥αMIs an eigenvalue, u, of a covariance matrixm∈￡M×1For eigenvectors corresponding to eigenvalues of the covariance matrix, Us＝[u1,u2,...,uK]，Σs＝diag{α1,α2,...,αK}，Un＝[uK+1,uK+2,...,uM]，Σn＝diag{αK+1,αK+2,...,αM}，UsAnd UnRespectively a signal subspace and a noise subspace.
Preferably, the spectrum function obtaining module obtains the spectrum function corresponding to each grid according to the noise subspace and the cross-coupling matrix between the array elements, specifically including,
using max dHQ-1(Θ) d obtaining a spectral function corresponding to each grid, wherein,
Figure GDA0003388351630000122
T(:,q)＝Jqa，a∈￡M×M，
Figure GDA0003388351630000123
d＝[1,0,...,0]T，q＝1,2,3...,Q， Q<m, C are cross-coupling matrices between array elements, UnIs a noise subspace, T ∈ CM×Q，c＝[c1,c2,...,cQ]TT (: q) is the q-th row of T, n is more than or equal to 1, and M is more than or equal to M.
Preferably, the module for obtaining DOA and mutual coupling coefficient obtains the mutual coupling coefficient between the array elements according to the estimated DOA, specifically including using a formula
Figure GDA0003388351630000124
And obtaining the mutual coupling coefficient between array elements, wherein,
Figure GDA0003388351630000125
for the mutual coupling coefficient, p is a constant,
Figure GDA0003388351630000126
is the estimated DOA.
It should be noted that the description of example 1 and example 2 is not repeated, and they can be referred to each other.
The invention discloses a method and a system for estimating and calibrating arbitrary array manifold DOA under a cross coupling condition, wherein an array signal is obtained, a covariance matrix corresponding to the array signal is obtained according to the array signal estimation, and the covariance matrix is subjected to characteristic decomposition to obtain a noise subspace; determining the angle search range of the DOA, generating a group of grids according to the angle search range of the DOA, and acquiring a spectrum function corresponding to each grid according to the noise subspace and a mutual coupling matrix between array elements; and estimating to obtain DOA according to the peak value of the spectrum function corresponding to each grid, and acquiring the mutual coupling coefficient between array elements by the estimated DOA, so that the DOA estimation and the mutual coupling calibration of any array manifold under the mutual coupling condition are realized simply, and the method can be applied to a real-time system.
Those skilled in the art will appreciate that all or part of the flow of the method implementing the above embodiments may be implemented by a computer program, which is stored in a computer readable storage medium, to instruct related hardware. The computer readable storage medium is a magnetic disk, an optical disk, a read-only memory or a random access memory.
The above-described embodiments of the present invention should not be construed as limiting the scope of the present invention. Any other corresponding changes and modifications made according to the technical idea of the present invention should be included in the protection scope of the claims of the present invention.

Claims (2)

1. A method for estimating and calibrating manifold DOA of any array under the condition of mutual coupling is characterized by comprising the following steps:
obtaining an array signal, estimating according to the array signal to obtain a covariance matrix corresponding to the array signal, and performing characteristic decomposition on the covariance matrix to obtain a noise subspace;
determining the angle search range of the DOA, generating a group of grids according to the angle search range of the DOA, and acquiring a spectrum function corresponding to each grid according to the noise subspace and a mutual coupling matrix between array elements;
performing feature decomposition on the covariance matrix to obtain a noise subspace, specifically including,
Figure FDA0003388351620000011
wherein the content of the first and second substances,
Figure FDA0003388351620000012
is a covariance matrix alpha1≥α2≥...≥αK≥αK+1≥...≥αMIs the eigenvalue of the covariance matrix,
Figure FDA0003388351620000013
for eigenvectors corresponding to eigenvalues of the covariance matrix, Us＝[u1,u2,...,uK]，Σs＝diag{α1,α2,...,αK}，Un＝[uK+1,uK+2,...,uM]，Σn＝diag{αK+1,αK+2,...,αM}，UsAnd UnRespectively a signal subspace and a noise subspace, wherein M is the number of array elements in the array antenna;
obtaining a spectrum function corresponding to each grid according to the noise subspace and the mutual coupling matrix among the array elements, specifically comprising,
using max dHQ-1(Θ) d obtaining a spectral function corresponding to each grid, wherein,
Figure FDA0003388351620000014
T(:,q)＝Jqa，
Figure FDA0003388351620000015
d＝[1,0,...,0]T，q＝1,2,3...,Q，Q<m, C are cross-coupling matrices between array elements, UnIn order to be a noise subspace,
Figure FDA0003388351620000016
c＝[c1,c2,..,cQ]Tt (: q) is the q-th row of T, n is more than or equal to 1, and M is more than or equal to M;
the specific form of the mutual coupling matrix is as follows:
Figure FDA0003388351620000021
estimating to obtain DOA according to the peak value of the spectrum function corresponding to each grid, and acquiring the mutual coupling coefficient between array elements according to the estimated DOA;
the mutual coupling coefficient between array elements is obtained by the estimated DOA, specifically including,
using formulas
Figure FDA0003388351620000022
And obtaining the mutual coupling coefficient between array elements, wherein,
Figure FDA0003388351620000023
for the mutual coupling coefficient, p is a constant,
Figure FDA0003388351620000024
is the estimated DOA.
2. A system for estimating and calibrating free array manifold DOA under the mutual coupling condition is characterized by comprising a noise subspace acquisition module, a spectral function acquisition module, a DOA and mutual coupling coefficient acquisition module,
the noise subspace acquisition module is used for acquiring an array signal, obtaining a covariance matrix corresponding to the array signal according to the array signal estimation, and performing feature decomposition on the covariance matrix to obtain a noise subspace;
the spectrum function acquisition module is used for determining the angle search range of the DOA, generating a group of grids according to the angle search range of the DOA, and acquiring a spectrum function corresponding to each grid according to the noise subspace and the cross coupling matrix among the array elements;
the noise subspace obtaining module is used for performing characteristic decomposition on the covariance matrix to obtain a noise subspace, and specifically comprises,
Figure FDA0003388351620000025
wherein the content of the first and second substances,
Figure FDA0003388351620000026
is a covariance matrix alpha1≥α2≥...≥αK≥αK+1≥...≥αMIs the eigenvalue of the covariance matrix,
Figure FDA0003388351620000027
for eigenvectors corresponding to eigenvalues of the covariance matrix, Us＝[u1,u2,...,uK]，Σs＝diag{α1,α2,...,αK}，Un＝[uK+1,uK+2,...,uM]，Σn＝diag{αK+1,αK+2,...,αM}，UsAnd UnRespectively a signal subspace and a noise subspace, wherein M is the number of array elements in the array antenna;
the spectrum function obtaining module obtains the spectrum function corresponding to each grid according to the noise subspace and the cross coupling matrix among the array elements, and specifically comprises,
using max dHQ-1(Θ) d obtaining a spectral function corresponding to each grid, wherein,
Figure FDA0003388351620000031
T(:,q)＝Jqa，
Figure FDA0003388351620000032
Figure FDA0003388351620000033
d＝[1,0,...,0]T，q＝1,2,3...,Q，Q<m, C are cross-coupling matrices between array elements, UnIn order to be a noise subspace,
Figure FDA0003388351620000034
c＝[c1,c2,...,cQ]Tt (: q) is the q-th row of T, n is more than or equal to 1, and M is more than or equal to M;
the specific form of the mutual coupling matrix is as follows:
Figure FDA0003388351620000035
the DOA and mutual coupling coefficient acquisition module is used for estimating and obtaining the DOA according to the peak value of the spectrum function corresponding to each grid and acquiring the mutual coupling coefficient between the array elements according to the estimated DOA;
the mutual coupling coefficient between array elements is obtained by the estimated DOA, specifically including,
using formulas
Figure FDA0003388351620000036
And obtaining the mutual coupling coefficient between array elements, wherein,
Figure FDA0003388351620000037
for the mutual coupling coefficient, p is a constant,
Figure FDA0003388351620000038
is the estimated DOA.
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
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CN115087881B (en) * 2020-06-01 2023-04-11 华为技术有限公司 Method and device for estimating angle of arrival (AOA)
CN112180327B (en) * 2020-09-04 2024-04-09 西北工业大学 Direct positioning method based on Doppler frequency shift under mutual coupling condition
CN112285641B (en) * 2020-09-16 2023-12-29 西安空间无线电技术研究所 ICA-based DOA (direction of arrival) estimation method and device
CN112305494B (en) * 2020-10-23 2023-12-12 北京邮电大学 Sensor position calibration method and device
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CN113589223B (en) * 2021-06-11 2023-05-05 南京邮电大学 Direction finding method based on nested array under mutual coupling condition
CN113625220A (en) * 2021-06-28 2021-11-09 台州学院 New method for quickly estimating direction of arrival and diffusion angle of multipath signal
CN113821907B (en) * 2021-08-19 2024-03-19 南京理工大学 Amplitude and phase automatic calibration method for large planar antenna array system
CN113777554A (en) * 2021-08-26 2021-12-10 南京航空航天大学 Two-dimensional DOA estimation method based on root finding Capon
CN113960525B (en) * 2021-10-15 2024-04-12 南京航空航天大学 Frequency hopping signal rapid direction finding method based on frequency domain TOEPLITZ matrix reconstruction
CN114113808B (en) * 2021-11-22 2023-08-15 杭州电子科技大学 DOA-polarization information joint estimation method based on incomplete electric vector sensor

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2293094A1 (en) * 2009-09-01 2011-03-09 Fujitsu Limited Method of estimating direction of arrival and apparatus thereof
CN105403871A (en) * 2015-10-28 2016-03-16 江苏大学 Bistatic MIMO radar array target angle estimation and mutual coupling error calibration method
CN106154217A (en) * 2016-07-12 2016-11-23 南京邮电大学 The method for self-calibrating eliminated based on spatial spectrum puppet peak during mutual coupling the unknown in ULA and UCA
CN108680891A (en) * 2018-01-05 2018-10-19 大连大学 The DOA estimation method of mutual coupling effect is considered under the conditions of non-uniform noise
CN109358312A (en) * 2018-11-13 2019-02-19 内蒙古科技大学 Determine method, apparatus, medium and the equipment of incoming signal arrival bearing

Family Cites Families (12)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP1777539B1 (en) * 2004-08-12 2013-01-09 Fujitsu Limited Radio wave arrival direction adaptive deduction tracking method and device
WO2007127182A2 (en) * 2006-04-25 2007-11-08 Incel Vision Inc. Noise reduction system and method
CN101272168B (en) * 2007-03-23 2012-08-15 中国科学院声学研究所 Signal sources estimation method and its DOA estimation method
US20090079646A1 (en) * 2007-09-21 2009-03-26 Harris Corporation Radio frequency device for unmixing polarized signals and associated methods
US8428897B2 (en) * 2008-04-08 2013-04-23 Massachusetts Institute Of Technology Method and apparatus for spectral cross coherence
US8576769B2 (en) * 2009-09-28 2013-11-05 Atc Technologies, Llc Systems and methods for adaptive interference cancellation beamforming
US9559417B1 (en) * 2010-10-29 2017-01-31 The Boeing Company Signal processing
US10386447B2 (en) * 2015-09-16 2019-08-20 Qatar University Method and apparatus for simple angle of arrival estimation
US10481242B2 (en) * 2015-09-25 2019-11-19 Texas Instruments Incorporated Method for joint antenna-array calibration and direction of arrival estimation for automotive applications
US11460558B2 (en) * 2017-07-20 2022-10-04 UNIVERSITé LAVAL Second-order detection method and system for optical ranging applications
JP6947054B2 (en) * 2018-01-24 2021-10-13 株式会社デンソー Radar device
WO2020037280A1 (en) * 2018-08-17 2020-02-20 Dts, Inc. Spatial audio signal decoder

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
EP2293094A1 (en) * 2009-09-01 2011-03-09 Fujitsu Limited Method of estimating direction of arrival and apparatus thereof
CN105403871A (en) * 2015-10-28 2016-03-16 江苏大学 Bistatic MIMO radar array target angle estimation and mutual coupling error calibration method
CN106154217A (en) * 2016-07-12 2016-11-23 南京邮电大学 The method for self-calibrating eliminated based on spatial spectrum puppet peak during mutual coupling the unknown in ULA and UCA
CN108680891A (en) * 2018-01-05 2018-10-19 大连大学 The DOA estimation method of mutual coupling effect is considered under the conditions of non-uniform noise
CN109358312A (en) * 2018-11-13 2019-02-19 内蒙古科技大学 Determine method, apparatus, medium and the equipment of incoming signal arrival bearing

Non-Patent Citations (4)

* Cited by examiner, † Cited by third party
Title
"DOA estimation in an antenna array with mutual coupling based on ESPRIT";Li Hao;《2013 International Workshop on Microwave and Millimeter Wave Circuits and System Technology》;20140515;全文 *
"Two-Dimensional Direction Finding Estimation for Uniform Rectangular Array with Unknown Mutual Coupling via Real-Valued PARAFAC Decomposition";Xu, Lingyun;《JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS》;20190331;第28卷(第3期);全文 *
"存在互耦情况下的阵列测向技术研究";吴晗;《中国优秀硕士学位论文全文数据库信息科技辑》;20171115;31-36 *
"非理想条件下DOA估计算法研究";刘婧;《中国博士学位论文全文数据库 信息科技辑》;20190115;70-73 *

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